The right to privacy was mentioned in Dobbs but only to simply say Roe was wrong to base legalizing abortion on a right to privacy. They never explained how it was wrong or why it was wrong. They simply stated that the 14th amendment didn't cover abortion.
From the text of Dobbs
******The Constitution makes no express reference to a right to obtain an abortion, but several constitutional provisions have been offered as potential homes for an implicit constitutional right. Roe held that the abortion right is part of a right to privacy that springs from the First, Fourth, Fifth, Ninth, and Fourteenth Amendments.
*******the Court finds the Fourteenth Amendment clearly does not protect the right to an abortion.
********the Due Process Clause of the Fourteenth Amendment. That provision has been held to guarantee some rights that are not mentioned in the Constitution, but any such right must be “deeply rooted in this Nation’s history and tradition” and “implicit in the concept of ordered liberty.” Washington v. Glucksberg, 521 U. S. 702, 721 (1997) (internal quotation marks omitted).
*******The Court finds that the right to abortion is not deeply rooted in the Nation’s history and tradition.
******** As to precedent, citing a broad array of cases, the Court (the RvW court not the present Court) found support for a constitutional “right of personal privacy.” Id., at 152. But Roe conflated the right to shield information from disclosure and the right to make and implement important personal decisions without governmental interference.
***** When the Court(the RvW court) summarized the basis for the scheme it imposed on the country,.......The scheme Roe produced looked like legislation, and the Court provided the sort of explanation that might be expected from a legislative body.
********Finally, the Court considers whether a right to obtain an abortion is part of a broader entrenched right that is supported by other precedents. The Court concludes the right to obtain an abortion cannot be justified as a component of such a right. Attempts to justify abortion through appeals to a broader right to autonomy and to define one’s “concept of existence” prove too much. Casey, 505 U. S., at 851. Those criteria, at a high level of generality, could license fundamental rights to illicit drug use, prostitution, and the like.
The Alito decision did not address privacy. They mentioned it and dismissed it without explaining why other than it might lead to legalized drug use and prostitution. Those are not compelling reasons to dismiss the right to make private decisions about personal reproduction issues.
